1. **Problem statement:** We have a piecewise function $$h(x) = \begin{cases} -2x + 4 & \text{if } x \leq 1 \\ x^2 + 1 & \text{if } x > 1 \end{cases}$$ We need to find the value of $h(3)$. 2. **Identify which piece to use:** Since $3 > 1$, we use the second piece of the function: $$h(x) = x^2 + 1$$ 3. **Calculate $h(3)$:** Substitute $x=3$ into the second piece: $$h(3) = 3^2 + 1 = 9 + 1 = 10$$ 4. **Answer:** The value of $h(3)$ is 10. Therefore, the correct choice is (A) 10.